A Physics-Informed Probabilistic Machine-Learning Framework for Bearing-Capacity Prediction of Geogrid-Reinforced Stone Columns in Spatially Variable Soils

Abstract Geogrid-reinforced stone columns are widely used to improve the bearing capacity and settlement performance of foundations constructed over weak and compressible soils. Their response, however, is governed by complex nonlinear interactions among the surrounding soil, the granular column, the geogrid reinforcement, footing geometry, column arrangement, and the spatial variability of soil properties. Conventional analytical and deterministic numerical methods require considerable computational effort and generally cannot quantify the uncertainty associated with naturally heterogeneous ground conditions. This paper proposes a physics-informed probabilistic machine-learning (PIML) framework for predicting the ultimate bearing capacity of geogrid-reinforced stone-column foundations subjected to spatially variable soil conditions. A three-dimensional finite-element and random finite-element (RFEM) methodology is used to generate a high-fidelity synthetic database by systematically varying undrained shear strength, friction angle, unit weight, elastic modulus, coefficient of variation, scale of fluctuation, column diameter, spacing, length, area replacement ratio, geogrid tensile stiffness, reinforcement depth, and footing dimensions. Random fields represent the spatial variability of the foundation soil, and Monte Carlo simulation quantifies the resulting variability in bearing capacity and failure mechanism. The generated database is used to develop conventional machine-learning benchmark models and a physics-informed neural network in which geotechnical constraints are embedded in the loss function; a probabilistic output layer estimates both the expected bearing capacity and the associated prediction uncertainty. Model interpretation is performed using SHAP (SHapley Additive exPlanations) analysis, and reliability analysis is conducted on the predicted probability distribution to estimate the probability of bearing-capacity failure and the reliability index. The proposed methodology provides a computationally efficient surrogate for repeated RFEM analyses while retaining the fundamental geotechnical constraints of the problem, and is intended to support reliability-based design and performance assessment of geogrid-reinforced stone-column foundations in spatially heterogeneous soils.